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Bonjour
un abstract a été soumis dans le site SOCASTAT
par : NGOUFACK NGANDJI MARCEL LOIC
Sujet d’intérêt : MÉTHODES AVANCÉES EN STATISTIQUE
Message : Online Statistical Estimation via Bayesian Variational EM in
State-Space Models
Authors: Marcel Loïc Ngoufack, joint work with Prof. Patrice Takam Soh and Dr. Wilson
Toussile.
Abstract
The analysis of sequential data is a central challenge in many fields, including finance,
computational biology, and signal processing. State-space models are among the most suitable
tools for such data, as they distinguish between unobserved latent states and measurable
observations. However, inference in these models remains challenging, particularly when data
arrive sequentially and parameter uncertainty must be explicitly accounted for.While the
classical Expectation-Maximization (EM) algorithm remains the standard approach for
parameter estimation in state-space models, it requires access to the entire dataset and does
not quantify parameter uncertainty. Variational methods provide a tractable alternative. In
particular, Campbell et al. (2021) introduced an online variational inference algorithm based
on a backward decomposition of the posterior distribution and Bellman-type recursions for
Evidence Lower Bound (ELBO) optimization. However, this approach was not formulated
within a Bayesian framework.In this work, we propose a Bayesian extension of this algorithm
by combining mean-field variational factorization with the backward decomposition
introduced by Campbell et al. (2021). The resulting algorithm recursively updates, upon the
arrival of each new observation, the variational distributions of both latent states and model
parameters while explicitly accounting for parameter uncertainty. This provides a Bayesian,
scalable, and theoretically principled extension of Campbell’s algorithm for online inference
in state-space models.Numerical experiments illustrate the effectiveness and performance of
the proposed method.
—
Merci.
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